(1) Simplify
(i) [x (x + 1)/(x - 2)] + [x(1 - x)/(x - 2)] Solution
(ii) (x + 2)/(x + 3) + (x - 1)/(x - 2) Solution
(iii) [x^{3}/(x - y)] + [y^{3}/(y - x)] Solution
(2) Simplify
(i) [(2x + 1)(x - 2)/(x - 4)] - [(2x^{2} - 5x + 2)/(x - 4)]
(ii) 4x/(x^{2} - 1) - (x + 1)/(x - 1) Solution
(3) Subtract 1/(x^{2} + 2) from (2x^{3} + x^{2} + 3)/(x^{2} + 2)^{2}
(4) Which rational expression should be subtracted from
(x^{2} + 6x + 8)/(x^{3} + 8) to get 3/(x^{2} - 2x + 4)
(5) If A = (2x + 1)/(2x - 1) and B = (2x - 1)/(2x + 1) find 1/(A - B) - 2B/(A^{2} - B^{2}) Solution
(6) If A = x/(x + 1), B = 1/(x + 1), prove that
((A + B)^{2} + (A- B)^{2})/(A ÷ B) = 2(x^{2} + 1)/x(x + 1)^{2}
(7) Pari needs 4 hours to complete a work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together? Solution
(8) Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ₹ 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy? Solution
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